Nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication, biological, economical, and neural network applications. For this class of positive systems, we provide conditions that guarantee existence, uniqueness and stability of strictly positive equilibria. These conditions can be formulated directly in terms of the spectral radius of the Jacobian of the system. If control inputs are available, then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant.

This paper discusses effects of nonlinearities in black box identification of one axis of a robot. The used data come from a commercial ABB robot, IRB1400. A three-mass flexible model for the robot was built in MathModelica. The nonlinearities in the model are nonlinear friction and backlash in the gear box.

A novel frequency and modal domain formulation of the model updating problem is presented. Deviations in discrete frequency responses and eigenfrequencies, between the model to be updated and a reference model, constitute the criterion function. A successful updating thus results in a model with the reference's input-output relations at selected fre- quencies. The formulation is demonstrated to produce a criterion function with a global minimum having a large domain of attraction with respect to stiffness and mass variations. The method relies on mode grouping and uses a new extended modal assurance criterion number (eMAC) for identifying related modes. A quadratic objective with inexpensive evaluation of approximate Hessians give a rapid convergence to a minimum by the use of a regularized Gauss-Newton method. Physical bounds on parameters and complementary data, such as structural weight, are treated by imposing set constraints and linear equality constraints. Efficient function computation is obtained by model reduction using a moderately sized base of modes which is recomputed during the minimization. Statistical properties of updated parameters are discussed. A verification example show the performance of the method.

Using data from extensive vibrational tests of the new aircraft Saab 2000 three different methods for vibration analysis are studied. These methods are ERA (eigensystem realization algorithm), N4SID (a subspace method) and PEM (prediction error approach). We find that both the ERA and N4SID methods give good initial model parameter estimates that can be further improved by the use of PEM. We also find that all methods give good insights into the vibrational modes.

Kalman filters have been used by SMHI to improve the quality of their forecasts. Until now they have used a linear underlying model to do this. In this thesis it is investigated whether the performance can be improved by the use of nonlinear models such as polynomials and neural networks. The results suggest that an improvement is hard to achieve by this approach and that it is likely not worth the effort to implement a nonlinear model.

We present a system covering the complete process for automatic ground target recognition, from sensor data to the user interface, i.e., from low level image processing to high level situation analysis. The system is based on a query language and a query processor, and includes target detection, target recognition, data fusion, presentation and situation analysis. This paper focuses on target recognition and its interaction with the query processor. The target recognitionis executed in sensor nodes, each containing a sensor and the corresponding signal/image processing algorithms. New sensors and algorithms are easily added to the system. The processing of sensor data is performed in two steps; attribute estimation and matching. First, several attributes, like orientation and dimensions, are estimated from the (unknown but detected) targets. These estimates are used to select the models of interest in a matching step, where the targetis matched with a number of target models. Several methods and sensor data types are used in both steps, and data is fused after each step. Experiments have been performed using sensor data from laser radar, thermal and visual cameras. Promising results are reported, demonstrating the capabilities of the target recognition algorithms, the advantages of the two-level data fusion and the query-based system.

We study the sequential identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility is constructed. The systems parameters are sequentially estimated with the aid of parallel filtering algorithm. To improve the estimation performance for unknown parameters, the new resampling procedure is proposed. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

We study the identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility and its systems parameters is constructed. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

With the rising popularity of ROVs and other UV solutions, more robust and high performance controllers have become a necessity. A model of the ROV or UV can be a valuable tool during control synthesis. The main objective of this thesis was to use a model in design and development of controllers for an ROV.

In this thesis, an ROV from Blue Robotics was used. The ROV was equipped with 6 thrusters placed such that the ROV was capable of moving in 6-DOFs. The ROV was further equipped with an IMU, two pressure sensors and a magnetometer. The ROV platform was further developed with EKF-based sensor fusion, a control system and manual control capabilities.

To model the ROV, the framework of Fossen (2011) was used. The model was estimated using two different methods, the prediction-error method and an EKF-based method. Using the prediction-error method, it was found that the initial states of the quaternions had a large impact on the estimated parameters and the overall fit to validation data. A Kalman smoother was used to estimate the initial states. To circumvent the problems with the initial quaternions, an \abbrEKF was implemented to estimate the model parameters. The EKF estimator was less sensitive to deviations in the initial states and produced a better result than the prediction-error method. The resulting model was compared to validation data and described the angular velocities well with around 70 % fit.

The estimated model was used to implement feedback linearisation which was used in conjunction with an attitude controller and an angular velocity controller. Furthermore, a depth controller was developed and tuned without the use of the model. Performance of the controllers was tested both in real tests and simulations. The angular velocity controller using feedback linearisation achieved good reference tracking. However, the attitude controller could not stabilise the system while using feedback linearisation. Both controllers' performance could be improved further by tuning the controllers' parameters during tests.

The fact that the feedback linearisation made the ROV unstable, indicates that the attitude model is not good enough for use in feedback linearisation. To achieve stability, the magnitude of the parameters in the feedback linearisation were scaled down. The assumption that the ROV's center of rotation coincides with the placement of the ROV's center of gravity was presented as a possible source of error.

In conclusion, good performance was achieved using the angular velocity controller. The ROV was easier to control with the angular velocity controller engaged compared to controlling it in open loop. More work is needed with the model to get acceptable performance from the attitude controller. Experiments to estimate the center of rotation and the center of gravity of the ROV may be helpful when further improving the model.

The reference frame theory constitutes an essential aspect of electric machine analysis and control. In this study, apart from the conventional applications, it is reported that the reference frame theory approach can successfully be applied to real-time fault diagnosis of electric machinery systems as a powerful toolbox to find the magnitude and phase quantities of fault signatures with good precision as well. The basic idea is to convert the associated fault signature to a dc quantity, followed by the computation of the signals average in the fault reference frame to filter out the rest of the signal harmonics, i.e., its ac components. As a natural consequence of this, neither a notch filter nor a low-pass filter is required to eliminate fundamental component or noise content. Since the incipient fault mechanisms have been studied for a long time, the motor fault signature frequencies and fault models are very well-known. Therefore, ignoring all other components, the proposed method focuses only on certain fault signatures in the current spectrum depending on the examined motor fault. Broken rotor bar and eccentricity faults are experimentally tested online using a TMS320F2812 digital signal processor (DSP) to prove the effectiveness of the proposed method. In this application, only the readily available drive hardware is used without employing additional components such as analog filters, signal conditioning board, external sensors, etc. As the motor drive processing unit, the DSP is utilized both for motor control and fault detection purposes, providing instantaneous fault information. The proposed algorithm processes the measured data in real time to avoid buffering and large-size memory needed in order to enhance the practicability of this method. Due to the short-time convergence capability of the algorithm, the fault status is updated in each second. The immunity of the algorithm against non-ideal cases such as measurement offset errors and phase unbalance is theoretically and experimentally verified. Being a model-independent fault analyzer, this method can be applied to all multiphase and single-phase motors.

The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the lest-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.

The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the lest-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.

The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.

The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).

This master thesis studies the problem of parameter identification for system biology. Two methods have been studied. The method of interval analysis uses subpaving as a class of objects to manipulate and store inner and outer approximations of compact sets. This method works well with the model given as a system of differential equations, but has its limitations, since the analytical expression for the solution to the ODE is not always obtainable, which is needed for constructing the inclusion function. The other method, studied, is SDP-relaxation of a nonlinear and non-convex feasibility problem. This method, implemented in the toolbox bio.SDP, works with system of difference equations, obtained using the Euler discretization method. The discretization method is not exact, raising the need of bounding this discretization error. Several methods for bounding this error has been studied. The method of ∞-norm optimization, also called worst-case-∞-norm is applied on the one-step error estimation method.

The methods have been illustrated solving two system biological problems and the resulting SCP have been compared.

Modelica is a multi-domain and equation-based modeling language. Modelica is based on object-oriented principles and non-causal modeling. The language is constructed to facilitate reuse and decompose models. The models and the modellibrary can modified to design a new nonlinear components.

Object-oriented modeling is an excellent way to analyze and study large complex heterogeneous physical systems. The object-oriented modeling approach build on reusing and decomposition of models and non-causal modeling.

Modeling physical systems often leads to a DAE system with index 2 or 3. It is required to use automated symbolic manipulation of the DAE system to do the simulation.

Modelica need a compiler tool to run the simulation. Dymola is the dominating tool on the market. Through a graphic editor the user can easily model and simulate the physical system.

This study proposes a new model which is fully specified for automated seizure onset detection and seizure onset prediction based on electroencephalography (EEG) measurements. We processed two archetypal EEG databases, Freiburg (intracranial EEG) and CHB-MIT (scalp EEG), to find if our model could outperform the state-of-the art models. Four key components define our model: (1) multiscale principal component analysis for EEG de-noising, (2) EEG signal decomposition using either empirical mode decomposition, discrete wavelet transform or wavelet packet decomposition, (3) statistical measures to extract relevant features, (4) machine learning algorithms. Our model achieved overall accuracy of 100% in ictal vs. inter-ictal EEG for both databases. In seizure onset prediction, it could discriminate between inter-ictal, pre-ictal, and ictal EEG with the accuracy of 99.77%, and between inter-ictal and pre-ictal EEG states with the accuracy of 99.70%. The proposed model is general and should prove applicable to other classification tasks including detection and prediction regarding bio-signals such as EMG and ECG. (C) 2017 Elsevier Ltd. All rights reserved.

We still have very little knowledge about how ourbrains decouple different sound sources, which is known assolving the cocktail party problem. Several approaches; includingERP, time-frequency analysis and, more recently, regression andstimulus reconstruction approaches; have been suggested forsolving this problem. In this work, we study the problem ofcorrelating of EEG signals to different sets of sound sources withthe goal of identifying the single source to which the listener isattending. Here, we propose a method for finding the number ofparameters needed in a regression model to avoid overlearning,which is necessary for determining the attended sound sourcewith high confidence in order to solve the cocktail party problem.

Sleep scoring is used as a diagnostic technique in the diagnosis and treatment of sleep disorders. Automated sleep scoring is crucial, since the large volume of data should be analyzed visually by the sleep specialists which is burdensome, time-consuming tedious, subjective, and error prone. Therefore, automated sleep stage classification is a crucial step in sleep research and sleep disorder diagnosis. In this paper, a robust system, consisting of three modules, is proposed for automated classification of sleep stages from the single-channel electroencephalogram (EEG). In the first module, signals taken from Pz-Oz electrode were denoised using multiscale principal component analysis. In the second module, the most informative features are extracted using discrete wavelet transform (DWT), and then, statistical values of DWT subbands are calculated. In the third module, extracted features were fed into an ensemble classifier, which can be called as rotational support vector machine (RotSVM). The proposed classifier combines advantages of the principal component analysis and SVM to improve classification performances of the traditional SVM. The sensitivity and accuracy values across all subjects were 84.46% and 91.1%, respectively, for the five-stage sleep classification with Cohens kappa coefficient of 0.88. Obtained classification performance results indicate that, it is possible to have an efficient sleep monitoring system with a single-channel EEG, and can be used effectively in medical and home-care applications.

In this study, Random Forests (RF) classifier is proposed for ECG heartbeat signal classification in diagnosis of heart arrhythmia. Discrete wavelet transform (DWT) is used to decompose ECG signals into different successive frequency bands. A set of different statistical features were extracted from the obtained frequency bands to denote the distribution of wavelet coefficients. This study shows that RF classifier achieves superior performances compared to other decision tree methods using 10-fold cross-validation for the ECG datasets and the obtained results suggest that further significant improvements in terms of classification accuracy can be accomplished by the proposed classification system. Accurate ECG signal classification is the major requirement for detection of all arrhythmia types. Performances of the proposed system have been evaluated on two different databases, namely MIT-BIH database and St. -Petersburg Institute of Cardiological Technics 12-lead Arrhythmia Database. For MIT-BIH database, RF classifier yielded an overall accuracy 99.33 % against 98.44 and 98.67 % for the C4.5 and CART classifiers, respectively. For St. -Petersburg Institute of Cardiological Technics 12-lead Arrhythmia Database, RF classifier yielded an overall accuracy 99.95 % against 99.80 % for both C4.5 and CART classifiers, respectively. The combined model with multiscale principal component analysis (MSPCA) de-noising, discrete wavelet transform (DWT) and RF classifier also achieves better performance with the area under the receiver operating characteristic (ROC) curve (AUC) and F- measure equal to 0.999 and 0.993 for MIT-BIH database and 1 and 0.999 for and St. Petersburg Institute of Cardiological Technics 12-lead Arrhythmia Database, respectively. Obtained results demonstrate that the proposed system has capacity for reliable classification of ECG signals, and to assist the clinicians for making an accurate diagnosis of cardiovascular disorders (CVDs).

Mapping is a central and common task in robotics research. Building an accurate map without human assistance provides several applications such as space missions, search and rescue, surveillance and can be used in dangerous areas. One application for robotic mapping is to measure changes in terrain volume. In Sweden there are over a hundred landfills that are regulated by laws that says that the growth of the landfill has to be measured at least once a year.

In this thesis, a preliminary study of methods for measuring terrain volume by the use of an Unmanned Aerial Vehicle (UAV) and a Light Detection And Ranging (LIDAR) sensor is done. Different techniques are tested, including data merging strategies and regression techniques by the use of Gaussian Processes. In the absence of real flight scenario data, an industrial robot has been used fordata acquisition. The result of the experiment was successful in measuring thevolume difference between scenarios in relation to the resolution of the LIDAR. However, for more accurate volume measurements and better evaluation of the algorithms, a better LIDAR is needed.

Human body motion capture systems based on inertial sensors (gyroscopes andaccelerometers) are able to track the relative motions in the body precisely, oftenwith the aid of supplementary sensors. The sensor measurements are combinedthrough a sensor fusion algorithm to create estimates of, among other parame-ters, position, velocity and orientation for each body segment. As this algorithmrequires integration of noisy measurements, some drift, especially in the positionestimate, is expected. Taking advantage of the knowledge about the tracked sub-ject, a human body, models have been developed that improve the estimates, butposition still displays drift over time.In this thesis, a GNSS receiver is added to the motion capture system to givea drift-free measurement of the position as well as a velocity measurement. Theinertial data and the GNSS data complements each other well, particularly interms of observability of global and relative motions. To enable the models of thehuman body at an early stage of the fusion of sensor data, an optimization basedmaximum a posteriori algorithm was used, which is also better suited for thenonlinear system tracked compared to the conventional method of using Kalmanfilters.One of the models that improves the position estimate greatly, without addingadditional sensing, is the contact detection, with which the velocity of a segmentis set to zero whenever it is considered stationary in comparison to the surround-ing environment, e.g. when a foot touches the ground. This thesis looks at botha scenario when this contact detection can be applied and a scenario where itcannot be applied, to see what possibilities an addition of GNSS sensor couldbring to the human body motion tracking case. The results display a notable im-provement in position, both with and without contact detection. Furthermore,the heading estimate is improved at a full-body scale and the solution makes theestimates depend less on acceleration bias estimation.These results show great potential for more accurate estimates outdoors andcould prove valuable for enabling motion tracking of scenarios where the contactdetection model cannot be used, such as e.g. biking.

A class of continuous-time dynamical systems able to sort a list of real numbers is introduced in this paper. The dynamical sorting is achieved in a completely distributed manner, by modifying a consensus problem, namely right multiplying a Laplacian matrix by a diagonal matrix of weights that represents the desired order. The sorting obtained is relative, i.e., a conservation law is imposed on the dynamics. It is shown that sorting can be achieved in finite-time even in a globally smooth way.

In a continuous-time nonlinear driftless control system, an involutive flow is a composition of input profiles that does not excite any Lie bracket. Such flow composition is trivial, as it corresponds to a "forth and back" cyclic motion obtained rewinding the system along the same path. The aim of this paper is to show that, on the contrary, when a (nonexact) discretization of the nonlinear driftless control system is steered along the same trivial input path, it produces a net motion, which is related to the gap between the discretization used and the exact discretization given by a Taylor expansion. These violations of involutivity can be used to provide an estimate of the local truncation error of numerical integration schemes. In the special case in which the state of the driftless control system admits a splitting into shape and phase variables, our result corresponds to saying that the geometric phases of the discretization need not obey an area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases. (C) 2017 Elsevier B.V. All rights reserved.

It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.

In a continuous-time nonlinear driftless control system, a geometric phase is a consequence of nonintegrability of the vector fields, and it describes how cyclic trajectories in shape space induce non-periodic motion in phase space, according to an area rule. The aim of this paper is to shown that geometric phases exist also for discrete-time driftless nonlinear control systems, but that unlike their continuous-time counterpart, they need not obey any area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases. When the discrete-time system is obtained through Euler discretization of a continuous-time system, it is shown that the zero-area geometric phase corresponds to the gap between the Euler discretization and an exact discretization of the continuous-time system.

In order to investigate the cases in which an externally positive discrete-time system fails to have a minimal positive realization, in this paper we introduce the notion of minimal eventually positive realization, fr which the state update matrix becomes positive after a certain power. This property captures the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. It is shown in the paper that whenever a minimal eventually positive realization exists, then the sequence of Markov parameters of the impulse response admits decimated subsequences for which minimal positive realizations exist and can be obtained by downsampling the eventually positive realization.

Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

The aim of this paper is to modify continuous-time bounded confidence opinion dynamics models so that "changes of opinion" (intended as changes of the sign of the initial states) are never induced during the evolution. Such sign invariance can be achieved by letting opinions of different sign localized near the origin interact negatively, or neglect each other, or even repel each other. In all cases, it is possible to obtain sign-preserving bounded confidence models with state-dependent connectivity and with a clustering behavior similar to that of a standard bounded confidence model. (C) 2018 Elsevier Ltd. All rights reserved.

In simple organisms like E. coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E. coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.

Being able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of ℝless thansupgreater thannless than/supgreater than.

For communities of agents which are not necessarily cooperating, distributed processes of opinion forming are naturally represented by signed graphs, with positive edges representing friendly and cooperative interactions and negative edges the corresponding antagonistic counterpart. Unlike for nonnegative graphs, the outcome of a dynamical system evolving on a signed graph is not obvious and it is in general difficult to characterize, even when the dynamics are linear. In this paper, we identify a significant class of signed graphs for which the linear dynamics are however predictable and show many analogies with positive dynamical systems. These cases correspond to adjacency matrices that are eventually positive, for which the Perron-Frobenius property still holds and implies the existence of an invariant cone contained inside the positive orthant. As examples of applications, we determine cases in which it is possible to anticipate or impose unanimity of opinion in decision/voting processes even in presence of stubborn agents, and show how it is possible to extend the PageRank algorithm to include negative links.

This paper deals with differentiated services in real-time systems. Tasks submitted to a real-time system are differentiated with respect to importance and QoS requirements. We use feedback control to enforce the requirements in QoS and ensure a hierarchical admission policy based on the importance of the tasks. The results show that the requirements are met during steady state when the workload is constant. The feedback control approach does not satisfactorily manage QoS when there is a sudden and significant workload change (transient state) due to the time-variant nature of the system. To address this, we present preliminary and promising results using adaptive control, and report on some challenges we are facing when applying the theory.

The intricacy of real-time data service management increases mainly due to the emergence of applications operating in open and unpredictable environments, increases in software complexity, and need for performance guarantees. In this paper we propose an approach for managing the quality of service of real-time databases that provide imprecise and differentiated services, and that operate in unpredictable environments. Transactions are classified into service classes according to their level of importance. Transactions within each service class are further classified into subclasses based on their quality of service requirements. In this way transactions are explicitly differentiated according to their importance and quality of service requests. The performance evaluation shows that during overloads the most important transactions are guaranteed to meet their deadlines and that reliable quality of service is provided even in the face of varying load and execution time estimation errors.

Operationally efficient radio networks typically feature a high degree of self-organization. This means less planning efforts and manual intervention, and a potential for better radio resource utilization when network elements adapts its operation to the observed local conditions. The focus in this paper is selfoptimization of the random access channel (RACH) in the 3G Long Term Evolution (LTE). A comprehensive tutorial about the RACH procedure is provided to span the complexity of the selfoptimization. Moreover, the paper addresses RACH key performance metrics and appropriate modeling of the various steps and components of the procedure. Finally, some coupling between parameters and key performance metrics as well as selfoptimization examples are presented together with a feasibility discussion. The main ambition with this workshop paper is to present and define a relevant set of self-optimization problems, rather than to provide a complete solution.

Future radio access networks are expected to show a high degree of self-organization. This paper addresses self-tuning of the random access channel (RACH) in the 3G Long Term Evolution (LTE). The feasibility of self-tuning is investigated by means of simulation, where the coupling between several parameters and the performance of RACH is provided. The conclusion of the simulations is that RACH self-tuning is indeed possible given that UE assisted measurements are available for the self-tuning mechanism.

In the control of continuous and physical systems, the controlled system is sampled sufficiently fast to capture the dynamics of the system. In general, this property cannot be applied to the control of computer systems as the measured variables are often computed over a data set, e.g., deadline miss ratio. In this paper we quantify the disturbance present in the measured variable as a function of the data set size and the sampling period, and we propose a feedback control structure that suppresses the measurement disturbance. The experiments we have carried out show that a controller using the proposed control structure outperforms a traditional control structure with regard to performance reliability.

In the control of continuous and physical systems, the controlled system is sampled sufficiently fast to capture the system dynamics. In general, this property cannot be applied to the control of computer systems as the measured variables are often computed over a data set, e.g., deadline miss ratio. In this paper we quantize the disturbance present in the measured variable as a function of the sampling period and we propose a measurement disturbance suppressive control structure. The experiments we have carried out show that a controller using the proposed control structure outperforms a traditional control structure with regard to performance reliability and adaptation.

In recent years a new class of soft real-time applications operating in unpredictable environments has emerged. Typical for these applications is that neither the resource requirements nor the arrival rates of service requests are known or available a priori. It has been shown that feedback control is very effective to support the specified performance of dynamic systems that are both resource insufficient and exhibit unpredictable workloads. To efficiently use feedback control scheduling it is necessary to have a model that adequately describes the behavior of the system. In this paper we experimentally evaluate the accuracy of four linear time-invariant models used in the design of feedback controllers. We introduce a model (DYN) that captures additional system dynamics, which a previously published model (STA) fails to include. The accuracy of the models are evaluated by validating the models with regard to measured data from the controlled system and through a set of experiments where we evaluate the performance of a set of feedback control schedulers tuned using these models. From our evaluations we conclude that second order models (e.g., DYN) are more accurate than first order models (e.g. STA). Further we show that controllers tuned using second order models perform better than controllers tuned using first order models.

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.

We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are computationally cheaper, but potentially weaker, than the standard semidefinite relaxation. Our numerical results show that the new relaxations often produce the same results as the standard semidefinite relaxation, but at a lower computational cost.

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.

The computational complexity for direction-of-arrival estimation using sensor arrays increases very rapidly with the number of sensors in the array. One way to lower the amount of computations is to employ some kind of reduction of the data dimension. This is usually accomplished by employing linear transformations for mapping full dimension data into a lower dimensional space. Different approaches for selecting these transformations have been proposed. In this paper, a transformation matrix is derived that makes it possible to theoretically attain the full-dimension Cramér-Rao bound also in the reduced space. A bound on the dimension of the reduced data set is given, above which it is always possible to obtain the same accuracy for the estimates of the source localizations, using the lower-dimension data, as that achievable by using the full dimension data. Furthermore, a method is devised for designing the transformation matrix. Numerical examples, using this design method, are presented, where the achievable performance of the (optimal) Weighted Subspace Fitting method with full dimension data is compared to the performance obtained with reduced dimension data. The problem of estimating parameters of sinusoidal signals from noisy data is also addressed by a direct application of the results derived herein.

The main topic of this thesis is model predictive control (MPC) of an unstable fighter aircraft. When flying it is important to be able to reach, but not exceed the aircraft limitations and to consider the physical boundaries on the control signals. MPC is a method for controlling a system while considering constraints on states and control signals by formulating it as an optimization problem. The drawback with MPC is the computational time needed and because of that, it is primarily developed for systems with a slowly varying dynamics.

Two different methods are chosen to speed up the process by making simplifications, approximations and exploiting the structure of the problem. The first method is an explicit method, performing most of the calculations offline. By solving the optimization problem for a number of data sets and thereafter training a neural network, it can be treated as a simpler function solved online. The second method is called fast MPC, in this case the entire optimization is done online. It uses Cholesky decomposition, backward-forward substitution and warm start to decrease the complexity and calculation time of the program.

Both methods perform reference tracking by solving an underdetermined system by minimizing the weighted norm of the control signals. Integral control is also implemented by using a Kalman filter to observe constant disturbances. An implementation was made in MATLAB for a discrete time linear model and in ARES, a simulation tool used at Saab Aeronautics, with a more accurate nonlinear model.

The result is a neural network function computed in tenth of a millisecond, a time independent of the size of the prediction horizon. The size of the fast MPC problem is however directly affected by the horizon and the computational time will never be as small, but it can be reduced to a couple of milliseconds at the cost of optimality.